1. Field of the Invention
The present invention relates in general to electronic signal processing and, in particular, to an apparatus and method for substantially canceling impulsive noise from various data sets. The disclosed apparatus and method has substantial utility in gas and oil exploration where electromagnetic borehole telemetry (EBT) signals are utilized in determining geophysical attributes of the land surrounding the particular wellhole.
2. Background Art
As with any signal processing, EBT signals unavoidably contain unwanted noise. Most of this unwanted noise varies with time and location due to varying surface conditions and the lithology of the areas of operation. Much of this noise has been removed through the use of adaptive filtering. One particular type of adaptive filtering utilizes a least mean square gradient search to adjust filter parameters toward cancellation of the unwanted noise.
While adaptive filters generally perform well where the processed signal is relatively undisturbed (i.e. contains much of the spectrum), these filters are incapable of removing impulsive noise. Impulsive noise can be thought of as power spikes of relatively infinitesimal duration. As such, this impulsive noise tends to be spread across the spectrum resulting in a noise floor above which the real data must use. This results in a lower signal-to-noise ratio, which is undesirable.
It has been known in the prior art that these impulsive noises must be removed prior to the adaptive filtering stage. One approach has used median filters. Median filters run a sliding window over the data and at each step filter the data by replacing the point in the middle of the window by the median of the points inside the window. For example, if one uses a three point window and the values inside are 12, 5 and 30, the value 5 is replaced by 12, which is the median value of the three points. For high sample rate data, the median filter works well, without introducing much distortion to data. For low sample rate cases, the median filter can introduce significant unwanted distortion. The distortion is large due to the small number of samples present per cycle of the sine wave. For any given change in time, the change in magnitude would then be large. The peak points look like spikes to the median filter and are flattened. This type of distortion is highly undesirable when one considers the large error values relative to the very small signals of interest that can be over 60 db below the noise amplitude.
Another possible filtering method with smaller total error is one in which the data is scanned and only changed if impulses are detected. The impulse data are replaced by a piecewise-linear estimated value calculated using two previous data points. Even though this method reduces the total error, it still does not result in acceptable estimates for the noisy data points.
An ideal filter for impulsive noise removal is one that removes only the impulses and that will not distort any other data points. After the impulses have been removed, they must be replaced by suitable values. Different types of estimators can be used for this purpose. For example, the new value may be set to the previous value, the median (using a conditional median filter, for instance) or a piece-wise linear estimate. These methods may be useful for high sample rate data however, for low sample rates, other methods that minimize the estimation error are needed.